A175617 Decimal expansion of product_{n>=2} (1-n^(-6)).

9, 8, 2, 6, 8, 4, 2, 7, 7, 7, 4, 2, 1, 9, 2, 5, 1, 8, 3, 2, 4, 4, 7, 5, 9, 1, 6, 2, 5, 7, 1, 3, 6, 3, 7, 3, 5, 1, 4, 8, 2, 8, 9, 9, 8, 4, 4, 9, 1, 9, 5, 5, 5, 1, 7, 9, 1, 6, 9, 3, 3, 9, 6, 5, 4, 4, 3, 7, 8, 7, 1, 0, 9, 0, 0, 3, 7, 0, 0, 8, 6, 2, 3, 6, 1, 8, 4, 8, 6, 6, 9, 9, 8, 0, 0, 7, 8, 4, 7, 5, 6, 1, 5, 7, 6

Offset

0,1

Links

Table of n, a(n) for n=0..104.

E. Weisstein, Infinite Product, Mathworld.

Formula

Equals product_{t=1..5} 1/Gamma(2-exp(Pi*i*t/3)), where i is the imaginary unit and Pi/3 = A019670.

Equals exp(Sum_{j>=1} (1 - zeta(6*j))/j). - Vaclav Kotesovec, Apr 27 2020

Example

0.9826842777...

Maple

cosh(Pi*sqrt(3)/2)^2/6/Pi^2 ; evalf(%) ;

Mathematica

RealDigits[(1 + Cosh[Sqrt[3]*Pi])/(12*Pi^2), 10, 105] // First (* Jean-François Alcover, Feb 12 2013 *)

Prog

(PARI) exp(suminf(j=1, (1 - zeta(6*j))/j)) \\ Vaclav Kotesovec, Apr 27 2020

Crossrefs

Cf. A109219, A175615, A175619, A144665, A258871.

Sequence in context: A092172 A133619 A276499 * A111765 A111509 A157258

Adjacent sequences: A175614 A175615 A175616 * A175618 A175619 A175620

Keyword

cons,easy,nonn

Author

R. J. Mathar, Jul 26 2010

Status

approved